Abstract
The distributed aggregation of simple aggregates such as minima/maxima, counts, sums and averages have been studied in the past and are important tools for distributed algorithms and network coordination. Nonetheless, this kind of aggregates may not be comprehensive enough to characterize biased data distributions or when in presence of outliers, making the case for richer estimates. This work presents Spectra, a distributed algorithm for the estimation of distribution functions over large scale networks. The estimate is available at all nodes and the technique depicts important properties: robustness when exposed to high levels of message loss, fast convergence speed and fine precision in the estimate. It can also dynamically cope with changes of the sampled local property and with churn, without requiring restarts. The proposed approach is experimentally evaluated and contrasted to a competing state of the art distribution aggregation technique. © 2012 IFIP International Federation for Information Processing.

Abstract
Data aggregation plays an important role in the design of scalable systems, allowing the determination of meaningful system-wide properties to direct the execution of distributed applications. In the particular case of wireless sensor networks, data collection is often only practicable if aggregation is performed. Several aggregation algorithms have been proposed in the last few years, exhibiting different properties in terms of accuracy, speed and communication tradeoffs. Nonetheless, existing approaches are found lacking in terms of fault tolerance. In this paper, we introduce a novel fault-tolerant averaging based data aggregation algorithm. It tolerates substantial message loss (link failures), while competing algorithms in the same class can be affected by a Single lost message. The algorithm is based on manipulating flows (in the graph theoretical sense), that are updated using idempotent messages, providing it with unique robustness capabilities. Furthermore, evaluation results obtained by comparing it with other averaging approaches have revealed that it outperforms them in terms of time and message complexity.

Abstract
Flow-Updating (FU) is a fault-tolerant technique that has proved to be efficient in practice for the distributed computation of aggregate functions in communication networks where individual processors do not have access to global information. Previous distributed aggregation protocols, based on repeated sharing of input values (or mass) among processors, sometimes called Mass-Distribution (MD) protocols, are not resilient to communication failures (or message loss) because such failures yield a loss of mass. In this paper, we present a protocol which we call Mass-Distribution with Flow-Updating (MDFU). We obtain MDFU by applying FU techniques to classic MD. We analyze the convergence time of MDFU showing that stochastic message loss produces low overhead. This is the first convergence proof of an FU-based algorithm. We evaluate MDFU experimentally, comparing it with previous MD and FU protocols, and verifying the behavior predicted by the analysis. Finally, given that MDFU incurs a fixed deviation proportional to the message-loss rate, we adjust the accuracy of MDFU heuristically in a new protocol called MDFU with Linear Prediction (MDFU-LP). The evaluation shows that both MDFU and MDFU-LP behave very well in practice, even under high rates of message loss and even changing the input values dynamically.

Abstract